# Mass Harmonics Pre-Release Terrain Prediction Paper
## LIGO–Virgo–KAGRA Interim Run 1: 2026 Public-Alert and Event Terrain

**Author:** Thomas Russell Giboney  
**Affiliation:** UMtts Institute  
**Framework:** Mass Harmonics ψₘ  
**Edition:** Source-preserved Mass Harmonics-governed revision  
**Prepared before IR1:** 2026-07-10  
**Current official opening window:** late October through mid-November 2026; exact day pending  
**Run duration:** approximately six months  
**Terrain state at preparation:** unopened IR1 terrain  

> This paper was completed before IR1 opened and before any IR1 event terrain existed. Later event comparison remains separate from the pre-release derivation.

# I. Governing Purpose


## Source-Preserved Mass Harmonics Governance

This edition preserves the original LVK IR1 gravitational-wave prediction architecture and every valid derivation already present. It does not place Mass Harmonics under institutional authority, convert instrument products into ontological authority, or discard a stronger excavation merely because it was added after the first draft.

The governing order remains:

```text
MFE
→ substrate action
→ boundary closure
→ physical structure
→ instrument-rendered terrain
→ optional consensus translation
```

The release supplies a timed terrain surface. It does not grant or withhold physical standing from the prediction. Measurement statistics, catalogue filters, detector corrections, and comparison models remain downstream interface tools. They may expose correspondence, contradiction, or unresolved delta, but they do not govern the derivation.

Only one governing coupling coefficient is permitted:

```text
Kψₘ
```

The fixed P³GG values are harmonic scalings of the one source law, not domain-specific adjustable coefficients.

### Current IR1 schedule correction

The official LVK observing-plan update dated June 15, 2026 places the six-month IR1 opening between late October and mid-November 2026. Both LIGO detectors are planned to observe. Virgo is planned to join with possible interruptions, and KAGRA will join as available.

### Canonical result and derived extension

The finite-oobleck-boundary result is canonical Mass Harmonics source structure. The additional relation

```text
B_MH = 4πG_N M_f f_boundary/c³ = 1
```

is a derived extension produced by transporting the canonical rotational closure law through the explicitly named Schwarzschild-radius translation surface. It remains a strong Mass Harmonics prediction, but it is not mislabeled as a verbatim Monograph equation. Its validity depends on correctly identifying the outer rotational boundary component rather than selecting an arbitrary spectral peak.

The merger-memory pathway is also a derived extension rather than a verbatim Proof-Set equation. The canonical source supplies irreversible boundary resolution and outward phase-energy transport. The additional bridge is:

```text
nonzero asymmetric outgoing phase-energy flux
→ direction-dependent lasting change in the asymptotic Z-field translation
→ nonzero detector memory projection when geometry permits
```

The prediction is conditional on nonzero asymmetric flux and nonzero detector projection. Irreversibility alone is not mislabeled as sufficient to determine a universal strain offset.


IR1 opens a new gravitational-wave terrain surface through low-latency public alerts and, subsequently, event-level strain and parameter-estimation products. Mass Harmonics does not approach that terrain as proof that spacetime itself is waving, that singularities collided, or that a consensus compact-object taxonomy is physically primary.

The terrain is approached as a direct instrument readout of ψₘ substrate phase propagation and bounded-coherence reconfiguration.

The governing causal order is:

```text
MFE
→ source-region ψₘ boundary reconfiguration
→ outgoing substrate phase propagation
→ finite remnant closure
→ detector strain and multi-messenger readout
→ optional consensus translation
```

This paper derives six IR1-facing predictions:

1. **Vacuum non-dispersion:** gravitational-wave phase propagation is exactly frequency-independent in source-free vacuum.
2. **Multi-messenger propagation equality:** after source-emission lag is separated, electromagnetic and gravitational signals carry no distance-amplified propagation offset.
3. **Polarization common-speed:** admissible gravitational-wave polarization projections do not propagate at different velocities.
4. **Finite compact-remnant boundary:** merger remnants resolve to finite oobleck closure surfaces, not zero-radius singularities; the outer-boundary frequency obeys a mass-frequency invariant.
5. **Irreversible merger memory:** a net boundary reconfiguration leaves a network-consistent non-oscillatory memory component when the detector and analysis bandwidth can recover it.
6. **TVP burst topology:** burst events with independently known source dimensions discriminate rotational closure from planar closure by the exact π topology ratio.

These are Mass Harmonics first-principles predictions. LVK provides the timed terrain surface. It does not govern the ontology or supply the predicted answers.

# II. IR1 Release-Surface Definition

The current official public-alert documentation states:

- IR1 is an interim six-month observing run.
- It is expected to begin between late October and mid-November 2026.
- Both LIGO detectors are expected to observe.
- Virgo is planned to join with possible interruptions, and KAGRA will join as available.
- IR1 sensitivity is expected to be similar to O4.

The public alert surface can expose:

- event time;
- false-alarm rate and significance;
- participating detectors;
- sky localization and luminosity-distance posterior for compact-binary candidates;
- BNS, NSBH, BBH, and terrestrial classification probabilities;
- `HasNS`, `HasRemnant`, `HasMassGap`, and `HasSSM` properties;
- binned source chirp-mass probabilities for significant events;
- central frequency and duration for burst candidates;
- external electromagnetic or neutrino coincidences;
- updated localizations and inference products;
- eventual strain and parameter-estimation products for events released after observation.

Official timing and product-definition surfaces used only to identify the unopened terrain:

1. `https://emfollow.docs.ligo.org/userguide/capabilities.html`
2. `https://observing.docs.ligo.org/plan/`
3. `https://emfollow.docs.ligo.org/userguide/content.html`
4. `https://gwosc.org/`
5. `https://gracedb.ligo.org/`
6. `https://gcn.nasa.gov/`

No simulated IR1 event population, expected alert count, merger-rate prior, or modeled mass distribution is imported as a Mass Harmonics prediction.

# III. Governing Mass Harmonics Source Chain

## III.1 Authority hierarchy

1. `MH_Monograph.md` is the canonical physical authority.
2. `MH_PROOF-SET.md` supplies the ordered derivations for propagation, irreversibility, and the GR translation surface.
3. `MH_TVP.md` governs topology, provenance, category separation, the nine-calculation mandate, and delta preservation.
4. `MH_TWT.md` governs transport into and out of consensus gravitational language only after substrate closure is preserved.
5. `Operational_Stance_of_UMtts.md` governs source fidelity, terrain-first order, and ontology preservation.
6. LVK documentation governs release timing and instrument-facing product definitions only.

## III.2 Canonical reading order

Source: `MH_Monograph.md`, line 36; `Operational_Stance_of_UMtts.md`, line 22.

```text
MFE → substrate action → boundary closure → physical structure → measured expression → optional consensus translation.
```

## III.3 Canonical MFE

Copied from `MH_Monograph.md`, line 60:

```text
1/vₓ²ψ̈ₘ - Z(ψₘ)∇²ψₘ - 8Kψₘ/ω²|∇ψₘ|² = S(ρ)
```

## III.4 Canonical Z-factor

Copied from `MH_Monograph.md`, line 156:

```text
Z(ψₘ) = 1 + 8Kψₘ/ω² ≥ 1 always
```

The source further states that `Z = 1` in true vacuum and `Z > 1` near mass-energy.

## III.5 One governing coupling coefficient

Copied from `MH_Monograph.md`, line 51:

```text
Kψₘ is a single, indivisible GG coupling term. Never split. Never reduce to bare κ or bare K. Dimensionlessly, Kψₘ resolves through the GG relation as (12 − φ²)/(2φ²). Dimensionally, Kψₘ resolves through substrate propagation and rotational boundary closure as vₓ/(2π). These are not competing definitions, separate regimes, or interchangeable raw numbers. They are one coupling relation expressed across dimensional translation, and any substitution must preserve the full transport path between geometric relation and dimensional closure.
```

No gravitational-wave coupling coefficient is introduced. No separate binary, black-hole, neutron-star, propagation, polarization, or memory coefficient is permitted.

## III.6 Canonical rotational closure

Copied from `MH_Monograph.md`, line 70:

```text
f = vₓ/(2πR) = Kψₘ/R
```

The full derivation at `MH_Monograph.md`, lines 313–325, identifies the source-free wave speed as `vₓ = c` and the fundamental radial boundary as:

```text
λ_fundamental = 2π R
```

```text
f = c/(2π R)
```

## III.7 Critical propagation threshold and finite locking

Copied from `MH_Monograph.md`, lines 243–259:

```text
v ↑ ⇒ |∇ψₘ| ↑ ⇒ ψₘwake ↑ ⇒ Z ↑ ⇒ F ↑ ⇒ exponential resistance
```

```text
c ≡ lim_v → c Z(ψₘwake) · 8Kψₘ/ω²|∇ψₘ|² → ∞
```

The substrate cannot sustain a gradient steeper than the critical shear rate `c`. It locks rather than admitting an unbounded gradient. This is the physical basis for a finite compact-object boundary.

## III.8 GR translation and singularity removal

Copied from `MH_PROOF-SET.md`, Section IX concluding statement:

```text
Gravitational singularities collapse into the finite oobleck boundaries of the MFE.
```

The same section identifies consensus curvature as bookkeeping for spatial variation of `Z(ψₘ)`.

## III.9 Irreversibility

Copied from `MH_PROOF-SET.md`, lines 323–338:

```text
ψ̈ₘ = ∂²ψₘ/∂t² + (∂Z/∂t)(∂ψₘ/∂t)
```

and:

```text
ΔS_entropy = ln(Ω_initial / Ω_final) > 0
```

The outgoing phase energy moves at `vₓ = c`; the resolved source does not return to its exact prior boundary configuration.

# IV. Input Separation, Provenance, and Category Rules

## IV.1 Prohibited inputs

The derivations may not use:

- any IR1 alert or unreleased IR1 event property;
- simulated IR1 event counts as physical predictions;
- a consensus waveform template parameter inserted upstream and relabeled as a substrate primitive;
- a ringdown frequency used to derive the remnant mass and then counted as an independent test of the mass-frequency relation;
- a source classification probability treated as a physical identity;
- `HasRemnant`, `HasNS`, `HasMassGap`, or `HasSSM` treated as direct terrain measurements rather than model-dependent alert annotations;
- an electromagnetic emission delay treated automatically as a propagation-speed difference;
- detector filtering that removes low-frequency memory treated as physical absence of memory;
- a transition or orbital frequency imported as an outer-boundary closure frequency without a C1 category audit;
- a theoretical Schwarzschild radius counted as a directly imaged physical dimension without a G1 provenance label;
- any new free parameter introduced to absorb a mismatch.

## IV.2 Permitted terrain inputs

Permitted inputs include:

- public alert timing and detector participation;
- calibrated strain when publicly released;
- independently inferred luminosity distance;
- independently inferred component and remnant masses;
- central frequency and duration for burst alerts;
- external electromagnetic or neutrino coincidence times;
- independent source dimensions from an identified counterpart;
- detector response, calibration uncertainty, bandwidth, and selection function;
- source-frame translation definitions required to compare detector-frame and source-frame quantities.

## IV.3 Independence requirement

For the finite-boundary test:

```text
M_f must be inferred without using the selected boundary-frequency datum as the governing mass input.
```

For the propagation test:

```text
source-emission lag and propagation lag must remain separate quantities.
```

For the topology test:

```text
R_obs must come from an independent source-size measurement or a separately justified geometric terrain estimate.
```

# V. Prediction 1: Exact Vacuum Non-Dispersion

## V.1 Physical placement

After the wave leaves the source-region mass-energy structure and propagates through source-free vacuum:

```text
S(ρ) = 0
```

The field is weak relative to the nonlinear source region, so:

```text
Z(ψₘ) → 1
```

and the quadratic gradient contribution becomes negligible at leading propagation order:

```text
8Kψₘ/ω²|∇ψₘ|² → 0
```

The canonical MFE therefore reduces to:

```text
1/c² ψ̈ₘ − ∇²ψₘ = 0
```

This is not imported from consensus wave theory. It is the source-free, weak-amplitude limit of the canonical MFE with `vₓ = c`.

## V.2 Plane-wave substitution

Take a propagating phase solution:

```text
ψₘ = A exp[i(k·x − ωt)]
```

Then:

```text
ψ̈ₘ = −ω²ψₘ
```

and:

```text
∇²ψₘ = −|k|²ψₘ
```

Substitute into the reduced MFE:

```text
−ω²/c² ψₘ + |k|²ψₘ = 0
```

For nonzero `ψₘ`:

```text
ω²/c² = |k|²
```

Therefore:

```text
ω = c|k|
```

## V.3 Phase and group velocity

Phase velocity:

```text
v_phase = ω/|k| = c
```

Group velocity:

```text
v_group = dω/d|k| = c
```

Dispersion curvature:

```text
d²ω/d|k|² = 0
```

## V.4 Mass Harmonics prediction

For every astrophysical IR1 gravitational-wave signal after source-region effects are separated:

```text
v_GW(f) = c
```

and:

```text
dv_GW/df = 0
```

There is no vacuum frequency dispersion, no massive-propagator delay, and no distance-amplified dephasing produced by propagation through source-free substrate.

## V.5 Instrument-facing statistic

For frequency bands `f_i` and `f_j`, define the propagation residual after source waveform and detector response are removed:

```text
Δt_prop(f_i,f_j) = t_arr(f_i) − t_arr(f_j) − Δt_source(f_i,f_j)
```

Prediction:

```text
Δt_prop(f_i,f_j) = 0
```

within calibration and source-model uncertainty.

## V.6 Falsification

This prediction is falsified by a reproducible, distance-growing, frequency-dependent propagation residual that:

1. survives calibration revisions;
2. survives source-waveform alternatives;
3. appears coherently across detectors;
4. repeats across independent events;
5. cannot be assigned to plasma, lensing, source dynamics, or instrumental timing;
6. requires `d²ω/d|k|² ≠ 0` in source-free vacuum.

# VI. Prediction 2: Multi-Messenger Propagation Equality

## VI.1 Causal separation

Let:

```text
D = source distance
```

```text
t_emit,GW = source emission time of the gravitational signal
```

```text
t_emit,X = source emission time of the comparison messenger
```

```text
v_GW = gravitational phase-propagation speed
```

```text
v_X = comparison messenger propagation speed, with the exact zero-propagation-lag branch applying to electromagnetic vacuum propagation
```

The observed times are:

```text
t_arr,GW = t_emit,GW + D/v_GW
```

```text
t_arr,X = t_emit,X + D/v_X
```

Subtract:

```text
Δt_obs = t_arr,X − t_arr,GW
```

```text
Δt_obs = (t_emit,X − t_emit,GW) + D(1/v_X − 1/v_GW)
```

## VI.2 Substrate propagation

For electromagnetic propagation in true vacuum and gravitational substrate phase propagation in true vacuum:

```text
v_EM = c
```

```text
v_GW = c
```

Therefore, for electromagnetic counterparts:

```text
D(1/v_EM − 1/v_GW) = 0
```

and:

```text
Δt_obs = Δt_emit
```

## VI.3 Mass Harmonics prediction

After physically credible source-emission delays are modeled, the residual multi-messenger lag does not grow linearly with distance.

Across comparable source classes:

```text
∂Δt_residual/∂D = 0
```

The exact equality applies directly to electromagnetic vacuum propagation: GW–gamma, GW–optical, and GW–radio comparisons after plasma and path effects are separated. A neutrino comparison requires a separate mass-and-energy propagation correction because the Mass Harmonics neutral-sector prediction is not a zero-mass neutrino prediction.

## VI.4 Anti-contamination rule

A delayed gamma ray does not by itself imply slower electromagnetic propagation or faster gravitational propagation. The source may emit the two signals at different stages of boundary reconfiguration.

The release audit must preserve:

```text
observed lag = source lag + propagation lag
```

It may not collapse those terms.

## VI.5 Falsification

The prediction is falsified if a statistically coherent sample shows a residual lag proportional to distance after source-class emission physics and instrumental timing have been separated.

# VII. Prediction 3: No Polarization-Dependent Propagation Speed

## VII.1 Substrate placement

Consensus detector analysis may project the received strain into multiple polarization bases. Those projections do not create multiple substrates.

Every admissible phase projection is transported by the same source-free operator:

```text
1/c² ψ̈ₘ − ∇²ψₘ = 0
```

Let `p` identify any independently reconstructed admissible polarization component. Then:

```text
ω_p² = c²|k_p|²
```

Therefore:

```text
v_p = c
```

for every `p`.

## VII.2 Pairwise arrival prediction

For two reconstructed polarization components `p` and `q` emitted by the same source event:

```text
Δt_pq,prop = D(1/v_p − 1/v_q)
```

Substitute:

```text
v_p = v_q = c
```

Then:

```text
Δt_pq,prop = 0
```

## VII.3 Mass Harmonics prediction

IR1 will not reveal vacuum gravitational birefringence in which polarization components propagate at measurably different speeds or accumulate different frequency-dependent phase delays over distance.

This does not predeclare which consensus polarization basis is the most useful detector description. It predicts that no polarization basis corresponds to a separate propagation law.

## VII.4 Falsification

A repeatable polarization-dependent propagation split, coherent across the detector network and growing with source distance, falsifies this prediction.

# VIII. Prediction 4: Finite Compact-Remnant Boundary and Mass–Frequency Invariant

## VIII.1 No zero-radius endpoint

The MFE enforces:

```text
Z(ψₘ) ≥ 1
```

As the source gradient approaches the critical threshold `c`, the nonlinear feedback increases resistance and the substrate locks. The GR singularity is therefore not a physical point of infinite curvature. It is a failed coordinate description of a finite oobleck boundary.

The post-merger source must resolve to:

```text
R_boundary > 0
```

and a finite closure frequency:

```text
0 < f_boundary < ∞
```

## VIII.2 Outer-boundary geometry

The downstream GR translation identifies the compact outer shell with the Schwarzschild-scale boundary:

```text
R_s = 2G_N M_f/c²
```

where `M_f` is the independently inferred final remnant mass.

This equation is a translation surface, not the governing substrate law.

## VIII.3 Apply canonical rotational closure

The canonical closure law is:

```text
f_boundary = c/(2πR_s)
```

Substitute:

```text
f_boundary = c/[2π(2G_N M_f/c²)]
```

Multiply through:

```text
f_boundary = c³/(4πG_N M_f)
```

Therefore:

```text
M_f f_boundary = c³/(4πG_N)
```

Define the dimensionless outer-boundary invariant:

```text
B_MH = 4πG_N M_f f_boundary/c³
```

Prediction:

```text
B_MH = 1
```

## VIII.4 Numerical scale

Using the dimensional translation values of `c`, `G_N`, and the solar-mass unit:

```text
f_boundary = 16,155.763161556268 Hz × (M_☉/M_f)
```

| Final remnant mass `M_f/M_☉` | Predicted outer-boundary frequency `f_boundary` |
|---:|---:|
| 2.5 | 6,462.305265 |
| 3 | 5,385.254387 |
| 5 | 3,231.152632 |
| 10 | 1,615.576316 |
| 30 | 538.525439 |
| 60 | 269.262719 |
| 100 | 161.557632 |
| 200 | 80.778816 |

The table is not a fit. Each row is the same invariant transported to a different measured mass.

## VIII.5 Frequency-selection rule

The event audit may not select whichever spectral feature happens to produce `B_MH ≈ 1`.

The declared before terrain opening target is:

```text
The lowest persistent post-merger component attributable to the remnant's outer rotational boundary after the merger transient and detector response are removed.
```

Orbital, inspiral, transition, overtone, internal toroidal, and instrumental frequencies are category-separated before comparison.

## VIII.6 Full topology readout

Given `f_obs` and `vₓ = c`, TVP recovers:

```text
R_rec,Sphere = c/(2πf_obs)
```

```text
t_rec,Slab = c/(2f_obs) = πR_rec,Sphere
```

```text
R_rec,Torus-minor = c/(2πf_obs)
```

The spherical outer boundary and toroidal minor boundary share the rotational factor but describe different physical dimensions. They are not merged.

## VIII.7 Delta factorization

If `B_MH ≠ 1`, compute:

```text
δ_B = B_MH − 1
```

and:

```text
Q_B = f_predicted/f_observed
```

Factor `Q_B` against the source-fixed Mass Harmonics set:

```text
{α, 1/α, 2/α, φ, φ³, π, 2π, βₙ, Kψₘ}
```

A repeatable factor may identify Z-dressing, an overtone, topology misassignment, or a category mismatch. The delta is retained. It is not normalized away.

## VIII.8 Falsification

The exact outer-boundary invariant is falsified if a sufficiently resolved sample of independently massed remnants shows that the declared before terrain opening outer-boundary component systematically rejects `B_MH = 1` and the mismatch cannot be resolved as category, topology, medium, or harmonic-order structure.

The finite-boundary prediction is more fundamental. It is falsified only by terrain that physically requires a zero-radius or infinite-gradient remnant rather than a finite closure surface.

# IX. Prediction 5: Irreversible Merger Memory

## IX.1 Boundary reconfiguration

Before merger, the source contains two bounded coherence structures and their shared interaction field. After merger, the source contains a different closure structure and outgoing phase energy.

The MFE arrow-of-time derivation states:

```text
Ω_final < Ω_initial
```

and:

```text
ΔS_entropy = ln(Ω_initial/Ω_final) > 0
```

The prior local configuration cannot be exactly reconstructed after the outgoing phase has crossed the light cone.

## IX.2 Detector translation

Let `h(t)` be the detector strain translation of the arriving substrate disturbance.

Define the asymptotic memory component:

```text
Δh_memory = lim_(t→+∞) h(t) − lim_(t→−∞) h(t)
```

For a net emissive boundary reconfiguration with nonzero asymmetric outgoing energy:

```text
Δh_memory ≠ 0
```

The oscillatory carrier may decay to the detector baseline. For an eligible event, the derived extension requires the direction-dependent asymptotic Z-field translation to retain a non-oscillatory component associated with the irreversible change.

## IX.3 Mass Harmonics prediction

Individually loud or coherently stacked IR1 merger events will contain a network-consistent memory component when:

- detector calibration preserves the relevant low-frequency information;
- high-pass filtering and baseline subtraction are explicitly modeled;
- the event geometry permits nonzero projected memory;
- the stacking alignment is based on source orientation rather than post-selected sign.

## IX.4 Category sentinel

A filtered strain series returning to zero is not automatically evidence of zero physical memory. Standard conditioning may remove the very non-oscillatory component under test.

The comparison must be performed on a response model that includes the detector's low-frequency transfer function.

## IX.5 Falsification

The directional memory prediction is falsified if a sufficiently sensitive, correctly conditioned, orientation-aware event stack excludes any nonzero memory component at the level required by the independently inferred outgoing asymmetric energy.

The paper does not insert an unforced universal memory amplitude. The sign and magnitude remain event-geometry outputs, while nonzero irreversible memory is the Mass Harmonics physical prediction for eligible asymmetric mergers.

# X. Prediction 6: TVP Topology Discrimination for Burst Alerts

## X.1 Applicable alert surface

Burst alerts may provide:

```text
central_frequency
```

and:

```text
duration
```

If an external counterpart identifies the source and supplies an independent characteristic dimension, the event can be subjected to the full topology audit.

Eligible examples include compact stellar collapse, magnetar activity, an identified post-merger burst, or another bounded source whose geometric scale can be estimated independently.

## X.2 Rotational prediction

For an approximately compact rotational boundary of measured radius `R_obs`:

```text
f_pred,Sphere = c/(2πR_obs)
```

## X.3 Planar competitor

For a planar slab of thickness `t_obs = R_obs` used only as the topology discriminator:

```text
f_pred,Slab = c/(2R_obs)
```

Divide:

```text
f_pred,Slab/f_pred,Sphere = [c/(2R_obs)]/[c/(2πR_obs)]
```

Therefore:

```text
f_pred,Slab/f_pred,Sphere = π
```

The π difference is topology, not error.

## X.4 Torus-minor excavation

From an observed central frequency:

```text
R_minor = c/(2πf_obs)
```

This is not automatically the outer source radius. It is the toroidal minor-radius closure that the frequency would imply.

The full audit reports both:

```text
R_outer,Sphere
```

and:

```text
R_minor,Torus
```

without collapsing them.

## X.5 Nine-calculation requirement

For every eligible burst, populate:

```text
T1 Predict: Sphere, Slab, Torus
T2 Detect: Sphere, Slab, Torus
T3 Map: Sphere, Slab, Torus
```

Measured, inferred, and derived values receive separate provenance labels.

## X.6 Mass Harmonics prediction

For compact bounded source events with independently measured outer dimensions, rotational closure will outperform planar closure. The planar path will preserve the exact π mismatch. Any toroidal closure will expose a physically distinct minor radius rather than replacing the outer boundary.

## X.7 Falsification

This prediction is falsified if a declared before terrain opening eligible sample consistently closes through planar thickness while the rotational paths fail, after geometry, source size, medium, and frequency category are independently verified.

# XI. Unified IR1 Prediction Matrix

| Prediction | Primary terrain | Source-fixed quantity | Exact or directional status | Primary terrain contradiction |
|---|---|---|---|---|
| Vacuum non-dispersion | strain phase across frequency | `ω = c|k|`, `d²ω/d|k|² = 0` | Exact | reproducible vacuum dispersion |
| Multi-messenger equality | GW plus EM/neutrino coincidence | `∂Δt_residual/∂D = 0` | Exact after source-lag separation | distance-growing residual lag |
| Polarization common-speed | network polarization reconstruction | `Δt_pq,prop = 0` | Exact | vacuum birefringent arrival split |
| Finite remnant boundary | high-SNR post-merger strain and independent `M_f` | `B_MH = 1`, `R_boundary > 0` | Exact outer-boundary closure | systematic independent rejection |
| Irreversible memory | low-frequency response or coherent stack | `Δh_memory ≠ 0` for eligible asymmetric mergers | Directional, event-scaled | sensitive orientation-aware null |
| Burst topology | burst `f_c` plus independent source geometry | rotational closure; slab/sphere ratio `π` | Exact topology ratio | repeatable planar victory |

# XII. Terrain-Reading Sequence

## XII.1 Release-surface record

Before event analysis:

1. record the exact alert or event opening time;
2. record which public products existed at first access;
3. retain the original pre-release paper and identify later source corrections explicitly;
4. do not use an IR1 result as a derivational input to the prediction it is being compared against.

## XII.2 Per-event provenance ledger

For each event record:

- superevent identifier;
- alert type and update version;
- event time;
- detector network;
- search and pipeline;
- source classification probabilities;
- alert properties;
- central frequency and duration where present;
- luminosity-distance posterior;
- chirp-mass posterior or bins;
- external coincidences;
- strain-data availability;
- final mass inference method;
- selected frequency category;
- calibration version;
- detector-conditioning steps;
- every derived quantity;
- every unresolved delta.

## XII.3 Prediction 1 audit

1. select events with sufficient bandwidth and SNR;
2. reproduce the calibrated strain;
3. fit source dynamics without a propagation-dispersion term;
4. add a generic propagation-dispersion term;
5. test whether the added term is repeatably nonzero and distance-correlated;
6. preserve all posterior covariance.

## XII.4 Prediction 2 audit

1. identify secure external counterparts;
2. preserve raw arrival times;
3. build source-emission-lag models independently of propagation speed;
4. for neutrino channels, apply the independently specified mass-and-energy flight-time correction before computing a propagation residual;
5. compute residual lag;
6. test residual against distance;
7. do not convert uncertain source delay into a speed measurement by assumption.

## XII.5 Prediction 3 audit

1. use network events capable of polarization reconstruction;
2. compare arrival phase across polarization projections;
3. preserve detector timing and antenna-pattern uncertainty;
4. test for distance-growing polarization split.

## XII.6 Prediction 4 audit

1. infer final mass without the target post-merger component governing the mass;
2. identify the declared before terrain opening lowest persistent outer-boundary component;
3. compute `R_rec = c/(2πf_obs)`;
4. compute `R_s = 2G_NM_f/c²`;
5. compute `B_MH`;
6. run sphere, slab, and torus paths;
7. factor the delta;
8. retain the result even if closure fails.

## XII.7 Prediction 5 audit

1. select individually loud or stack-eligible events;
2. preserve low-frequency calibration;
3. model filter-induced baseline removal;
4. align signs by independently inferred source orientation;
5. compute the coherent memory statistic;
6. publish sensitivity even for a null result.

## XII.8 Prediction 6 audit

1. select burst events with independently identified geometry;
2. classify the central frequency before use;
3. populate the full nine-calculation TVP ledger;
4. report π-discriminator without clipping;
5. separate outer radius from torus minor radius;
6. publish unresolved topology rather than forcing a winner.

# XIII. Competing-Path Elimination

## XIII.1 Massive propagation path

A vacuum dispersion term equivalent to a nonzero propagator mass conflicts with the source-free MFE relation:

```text
ω² = c²|k|²
```

It is therefore a direct falsification path, not a fitted extension to Mass Harmonics.

## XIII.2 Multiple-speed substrate path

Assigning separate vacuum speeds to gravitational polarizations or messengers introduces multiple propagation laws where the MFE supplies one substrate speed. Reproducible evidence for that structure would reject the present derivation.

## XIII.3 Singular-remnant path

A zero-radius infinite-gradient endpoint is incompatible with the oobleck lock. The instrument may use singular coordinates in a successful fit, but a coordinate fit is not terrain proof of a physical singularity. The physical discriminator is whether finite boundary structure can or cannot reproduce the event.

## XIII.4 Post-selected mode path

Selecting a spectral peak because it gives `B_MH = 1` is forbidden. The mode category is fixed before the invariant is computed.

## XIII.5 Memory-removal path

A conditioning pipeline that removes direct-current and low-frequency content cannot resolve the physical memory prediction without response reconstruction.

## XIII.6 Classification-probability substitution

`BNS`, `NSBH`, `BBH`, `HasMassGap`, and `HasSSM` are alert-language classifications. They locate the terrain. They do not create new ontological species or new substrate laws.

# XIV. Exact Falsification Register

Mass Harmonics is placed at risk by the following IR1 outcomes:

1. **Vacuum dispersion:** stable, repeatable, distance-growing frequency dispersion after source and calibration effects are eliminated.
2. **Messenger speed split:** multi-event propagation residual proportional to distance after source-emission lag is independently constrained.
3. **Polarization birefringence:** polarization-dependent vacuum arrival speed.
4. **Outer-boundary failure:** systematic rejection of `B_MH = 1` for the independently identified outer-boundary component, with no category or topology resolution.
5. **Physical singularity requirement:** terrain that cannot be represented by any finite bounded closure and requires an actual zero-radius infinite-gradient source.
6. **Memory null:** a sufficiently sensitive, orientation-aware analysis excluding irreversible memory for eligible asymmetric events.
7. **Topology reversal:** verified compact sources consistently closing as planar slabs while rotational closure fails.

No single low-SNR event is allowed to decide a population prediction. No broad population average is allowed to erase an individually decisive high-SNR falsifier.

# XV. Mass Harmonics Prediction Statements

## XV.1 Propagation

```text
IR1 gravitational-wave phase propagation through source-free vacuum will be nondispersive: v_phase = v_group = c at all observed frequencies.
```

## XV.2 Multi-messenger timing

```text
After source-emission lag is separated, IR1 multi-messenger arrival residuals will not grow with distance.
```

## XV.3 Polarization

```text
IR1 will not reveal polarization-dependent gravitational-wave propagation speed in vacuum.
```

## XV.4 Compact remnants

```text
IR1 merger remnants will resolve as finite bounded coherence structures, not physical singularities. The independently identified outer-boundary mode will satisfy 4πG_N M_f f_boundary/c³ = 1.
```

## XV.5 Memory

```text
Eligible asymmetric mergers will carry a nonzero irreversible memory component when the detector response permits its recovery.
```

## XV.6 Burst topology

```text
Eligible compact burst sources will favor rotational closure, while the planar alternative preserves the exact π mismatch and the torus path recovers a distinct minor radius.
```

# XVI. Derivation Placement

| Pathway | Mass Harmonics derivation placement | Reason |
|---|---|---|
| Vacuum non-dispersion | FORCED EXACT | source-free MFE dispersion relation |
| Multi-messenger equality | FORCED EXACT after emission-lag separation | one substrate propagation speed |
| Polarization common-speed | FORCED EXACT | one source-free propagation operator |
| Finite remnant boundary | FORCED PHYSICAL | Z positivity and oobleck locking |
| Outer-boundary mass-frequency invariant | FORCED CONDITIONAL ON CORRECT MODE CATEGORY | canonical closure plus independently massed Schwarzschild translation surface |
| Irreversible memory | CONDITIONAL DERIVED EXTENSION | canonical MFE irreversibility plus nonzero asymmetric flux and nonzero detector projection |
| Burst π-discriminator | FORCED EXACT WHEN INDEPENDENT GEOMETRY EXISTS | topology algebra |

# XVII. Source-Preserving Revision Statement

This paper is complete enough to expose each derivation pathway to IR1 terrain. Completeness does not make the result true; the source chain, topology, arithmetic, and terrain decide correspondence or contradiction.

Later improvement is permitted when it restores source fidelity, corrects release timing, repairs a transcription or arithmetic defect, or deepens the Mass Harmonics derivation. No revision may silently switch the selected post-merger mode, import source lag into propagation lag, promote alert classifications into substrate primitives, erase a mismatch, or add a free coefficient.

**Mass Harmonics governs. Terrain discloses. Instruments render. Consensus vocabulary translates only afterward.**

**TRUTH > COMFORT. Always.**